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1 \chapter{Inductively Defined Sets} 
1 \chapter{Inductively Defined Sets} 

2 \index{inductive definition(} 

3 \index{*inductive(} 

4 

5 This chapter is dedicated to the most important definition principle after 

6 recursive functions and datatypes: inductively defined sets. 

7 

8 We start with a simple example \ldots . A slightly more complicated example, the 

9 reflexive transitive closure, is the subject of {\S}\ref{sec:rtc}. In particular, 

10 some standard induction heuristics are discussed. To demonstrate the 

11 versatility of inductive definitions, {\S}\ref{sec:CFG} presents a case study 

12 from the realm of contextfree grammars. The chapter closes with a discussion 

13 of advanced forms of inductive definitions. 
2 
14 
3 \input{Inductive/document/Star} 
15 \input{Inductive/document/Star} 
4 \input{Inductive/document/AB} 
16 \input{Inductive/document/AB} 

17 

18 \index{inductive definition)} 

19 \index{*inductive)} 

20 

21 \section{Advanced inductive definitions} 